Italian Alex Vinatzer claimed the bronze while Alpine powerhouse Austria, who led the first run with Manuel Feller, ended the championships without a gold for the first time since 1987.
France's 2022 Olympic slalom champion Clement Noel was fourth, missing a medal by 0.03 seconds.
Kristoffersen went from 16th after the first run to strike gold with the fastest time on the second down the icy L'Eclipse piste on a sunny day in the French Alps.
His second run time of 51.66 left him 0.20 quicker than Ginnis, who had been equal second with Norway's Lucas Braathen after the first run. Vinatzer was a further 0.18 slower.
As Kristoffersen's wait in the leader's chair at the finish area went on and on, a string of medal contenders fell short under pressure.
Nobody was feeling it more than Feller, Austria's last hope of gold, who had crashed in the warm-up and needed painkillers before his first run.
Two years ago in Italy's Cortina d'Ampezzo the Austrians led the table with five golds but they leave Courchevel-Meribel with three silvers and four bronzes.
Switzerland topped the medal standings this time with three golds, three silvers and a bronze.
Ginnis, who has come back from repeated knee surgeries and said after starting 24th in the first run that he felt no pressure, moved to America at the age of 15 and competed previously for the U.S. ski team.
The 28-year-old was second in a World Cup slalom in Chamonix on Feb. 4 and that World Cup podium was also a first for his country.
"It feels unreal," his serviceman Gabriel Coulet told Eurosport. "He went to chase his dream for Greece after so many injuries and he never let go.
"He always had the speed but with all the hurdles he had in his life he could never really bring it to a big achievement like this...today his dream came true."
Norway's defending world champion Sebastian Foss-Solevaag finished 19th.
